System and method for an engine controller based on inverse dynamics of the engine

ABSTRACT

Systems and methods for controlling a gas turbine engine are provided. The system comprises an interface to a fuel flow metering valve for controlling a fuel flow to the engine in response to a fuel flow command and a controller connected to the interface and configured for outputting the fuel flow command to the fuel flow metering valve in accordance with a required fuel flow. The controller comprises a feedforward controller configured for receiving a requested engine speed and acceleration, obtaining a steady-state fuel flow for the requested engine speed and a relationship between fuel flow and gas generator speed, and determining the required fuel flow to obtain the requested engine acceleration as a function of the requested engine speed, the steady-state fuel flow, and the relationship between fuel flow and gas generator speed.

CROSS-REFERENCE TO RELATED APPLICATIONS

The application is a continuation of U.S. patent application Ser. No. 15/361,254, filed on Nov. 25, 2016 and granted to U.S. Pat. No. 10,221,776, which claims the benefit of U.S. Provisional Patent Application No. 62/371,019 filed on Aug. 4, 2016, the contents of which are hereby incorporated by reference.

TECHNICAL FIELD

The disclosure relates generally to the field of gas turbine engine control, and more particularly, to an engine controller with a feedforward controller.

BACKGROUND

Methodologies used for controlling the acceleration of a gas turbine engine shaft include the use of a feedback controller. However, there are challenges achieving a desired response time while maintaining a certain stability margin when using a feedback controller. To overcome this issue, a feedforward controller is used in conjunction with the feedback controller. The feedforward controller can decrease the response time without penalizing stability margin. The feedforward controller is typically tuned iteratively in test. This operation is repeated for an array of operating points covering the gas turbine engine flight envelope. This method, which requires iterative testing of the engine, is resource consuming and expensive when the flight envelope is large.

Improvements in control systems are therefore desirable.

SUMMARY

In accordance with one broad aspect, there is provided a system for controlling a gas turbine engine of an aircraft. The system comprises an interface to a fuel flow metering valve for controlling a fuel flow to the engine in response to a fuel flow command and a controller connected to the interface and configured for outputting the fuel flow command to the fuel flow metering valve in accordance with a required fuel flow. The controller comprises a feedforward controller configured for receiving a requested engine speed and engine acceleration, obtaining a steady-state fuel flow for the requested engine speed and a relationship between fuel flow and gas generator speed, and determining the required fuel flow to obtain the requested engine acceleration as a function of the requested engine speed, the steady-state fuel flow, and the relationship between fuel flow and gas generator speed.

In accordance with another broad aspect, there is provided a method for controlling a gas turbine engine. The method comprises receiving a requested engine speed and acceleration and obtaining a steady-state fuel flow for the requested engine speed and a relationship between fuel flow and gas generator speed. The method further comprises determining the required fuel flow to obtain the requested engine acceleration as a function of the requested engine speed, the steady-state fuel flow, and the relationship between fuel flow and gas generator speed and outputting a command to a fuel flow metering valve in accordance with the required fuel flow.

In accordance with yet another broad aspect, there is provided a non-transitory computer-readable medium having stored thereon program code executable by a processor for controlling a gas turbine engine. The program code comprises instructions for receiving a requested engine speed and acceleration and obtaining a steady-state fuel flow for the requested engine speed and a relationship between fuel flow and gas generator speed. The program code further comprises instructions for determining the required fuel flow to obtain the requested engine acceleration as a function of the requested engine speed, the steady-state fuel flow, and the relationship between fuel flow and gas generator speed and outputting a command to a fuel flow metering valve in accordance with the required fuel flow.

DESCRIPTION OF THE DRAWINGS

Reference is now made to the accompanying figures in which:

FIG. 1 is a schematic cross-sectional view of a gas turbine engine;

FIG. 2 is a block diagram of an example aircraft system;

FIG. 3 is a schematic diagram of an example controller for an engine; and

FIG. 4 is a schematic diagram of an example feedforward controller for an engine.

FIG. 5 is a flow chart of an example method performed by a controller.

FIG. 6 is a schematic diagram of an example controller.

DETAILED DESCRIPTION

FIG. 1 illustrates a gas turbine engine 10 of a type provided for use in subsonic flight, generally comprising in serial flow communication a fan 12 through which ambient air is propelled, a compressor section 14 for pressurizing the air, a combustor 16 in which the compressed air is mixed with fuel and ignited for generating an annular stream of hot combustion gases, and a turbine section 18 for extracting energy from the combustion gases. High pressure rotor(s) 20 of the turbine section 18 are drivingly engaged to high pressure rotor(s) 22 of the compressor section 14 through a high pressure shaft 24. Low pressure rotor(s) 26 of the turbine section 18 are drivingly engaged to the fan rotor 12 and to other low pressure rotor(s) (not shown) of the compressor section 14 through a low pressure shaft 28 extending within the high pressure shaft 24 and rotating independently therefrom. Although illustrated as a turbofan engine, the gas turbine engine 10 may alternatively be another type of engine, for example a turboshaft engine, also generally comprising in serial flow communication a compressor section, a combustor, and a turbine section, and a fan through which ambient air is propelled. A turboprop engine may also apply.

FIG. 2 illustrates the gas turbine engine 10 of FIG. 1 within an aircraft 200. Engine thrust is controlled by a full authority digital electronic control (FADEC) which regulates the speed of the high pressure rotor(s) 20, 22 and low pressure rotor(s) 26 in response to a pilot-operated thrust lever, ambient conditions, pilot selection and aircraft discrete inputs. For simplicity, only the main control system components of the FADEC, namely a controller or an electronic engine control (EEC) 202, a thrust lever 201, and a fuel flow metering valve 204, are illustrated. FADEC works by receiving multiple input variables of the current flight condition including air density, throttle lever position, engine temperatures, engine pressures, and many other parameters. The inputs are received by EEC 202 and analyzed multiple times per second. Engine operating parameters such as fuel flow, stator vane position, bleed valve position, and others may be computed from this data and applied as appropriate. The FADEC may be a single channel FADEC or a dual channel architecture.

The fuel flow metering valve or simply metering valve 204 is connected to the EEC 202 via an interface or connection 203. The fuel flow metering valve 204 is arranged to control a fuel flow to the engine in response to a fuel flow command from the EEC 202. The metering valve 204 is under direct control from EEC 202 and enables thrust control, in response to variable guide vane position demands and fuel flow demands. The metering valve 204 provides the engine 10 with fuel from a fuel source 206 at a required pressure and flow to permit control of engine power. EEC 202 comprises digital logic to energize the metering valve 204. Sensor data obtained for a low rotor and/or a high pressure rotor can provide information about the speed of the engine 10.

EEC 202 is a controller operationally connected to the fuel flow metering valve 204 via the interface 203 and configured to generate the signal representing the final fuel flow rate. For example, EEC 202 may comprise a feedforward controller 208 and a feedback controller 210. EEC 202 is configured to control the gas turbine shaft acceleration through fuel flow regulation. The feedforward controller 208 allows, in conjunction with the feedback controller 210, the tracking of the reference acceleration without the need for iterative gain tuning.

FIG. 3 shows an example implementation inside EEC 202 of a method to control gas turbine engine 10 in accordance with one embodiment EEC 202 includes a feedforward controller 208 and a feedback controller 210. A signal 215 representing a requested gas generator speed, denoted by Ngreq, is input to the feedforward controller 208. In some embodiments, Ngreq 215 is the requested gas generator shaft speed. Signal Ngreq 215 may be obtained from a data table or an outer control loop. For example, Ngreq 215 may be the Ng speed requested by the outer control loop to achieve a certain engine power level, or thrust level. Ngreq 215 may also be a speed value selected to avoid a given engine limitation. Feedforward controller 208 is configured to determine and output a feedforward fuel flow WF_(FF) 217. The feedforward fuel flow WF_(FF) 217 is used to compute a total fuel flow WF_(tot) and generate a fuel flow signal Nc 219. The fuel flow signal Nc 219 is then sent to the gas turbine engine 10, represented by plant model 220, as an actuator command for controlling gas turbine speed and acceleration.

In some embodiments, in order to limit engine acceleration to a certain threshold, the controller 202 receives a reference acceleration, such as the requested acceleration {dot over (N)}greq 222. A rate-limited gas generator speed NgreqRL 232 is obtained by applying the requested gas generator speed Ngreq 215 to rate-limiter 216 based on the the requested acceleration {dot over (N)}greq 222. This way, a time derivative of the rate-limited gas generator speed NgreqRL 232 does not exceed the requested acceleration Ngreq 222, thereby controlling acceleration of the engine 10. The feedforward fuel flow WF_(FF) 217 may then be determined based on the rate-limited gas generator speed NgreqRL 232. In some embodiments, the reference acceleration is obtained from a data table (not shown). The data table may be pre-determined based on characteristics of engine 10.

In some embodiments, the rate-limiter 216 is provided as part of feedforward controller 208, such that feedforward controller 208 may take Ngreq 215 and apply a rate limit accordingly.

In order to generate the fuel flow command Nc 219, a feedback controller 210 may also be implemented, together with the feedforward controller 208. The feedback controller 210 forms a closed loop, the feedforward controller 208 forms an open-loop. The feedback controller 210 may be any kind of suitable feedback controller such as a proportional-integral-derivative (PID) controller. A feedback fuel flow WF_(FB) 226 may be generated by the feedback controller 210 and sent to summation junction 218, together with the feedforward fuel flow WF_(FF) 217, to obtain WF_(tot), representing the total fuel flow. Total fuel flow WF_(tot) is used to generate the fuel flow command Nc 219.

In some embodiments, the feedback controller 210 takes as input an acceleration error {dot over (N)}g_(err) 224 that is determined as the difference between the requested acceleration {dot over (N)}g_(req) 222 and a filtered acceleration Ng 228. The requested acceleration {dot over (N)}g_(req) 222 and the filtered acceleration {dot over (N)}g 228 are sent to a subtraction junction 223 to compute the acceleration error {dot over (N)}g_(err) 224. The filtered acceleration {dot over (N)}g 228 is removed from the requested acceleration {dot over (N)}g_(req) 222 to result in the acceleration error {dot over (N)}g_(err) 224.

The filtered acceleration {dot over (N)}g 228 may be obtained by taking a gas generator speed Ng 221 and feeding it through a filtered derivative function 227, which may generate a numerical derivative. The gas generator speed Ng 221 may be obtained in a number of ways. For example, it may be a measured value of the gas turbine shaft speed obtained from gas engine 10. Alternatively, the gas generator speed Ng 221 may be an output of a plant model 220. The plant model 220 may be implemented based on a function representing suitable engine dynamics of engine 10, such as the transfer function:

$\frac{K}{{\tau\; s} + 1},$

where τ represents an estimated time constant of the plant model and K represents an estimated gain of the plant model. For example, all hardware involved in fuel delivery to the engine 10 and its respective relationships may be simplified and modelled in the plant model 220. The plant model 220 may take the fuel flow command Nc 219 as input and generate the gas generator speed Ng 221.

In accordance with some embodiments, a model-based feedforward controller 208 is used to control the acceleration of a gas turbine engine 10 based on engine behavior. For example, it may be modelled based on inverse dynamics of the engine. The model-based feedforward controller 208 may provide a lead time required to compensate for a lag of the engine.

In some embodiments, the engine behavior can be simplified by a linear model of the first-order as seen in equation (1) below. That is, the feedforward controller 208 may be an inverse dynamics feedforward controller based on an inverse relationship between a fuel flow and a speed of the gas turbine engine. This relationship may be modelled as equation (1) below:

$\begin{matrix} {{{P(s)} = {\frac{\delta\;{{Ng}(s)}}{\delta\;{{Wf}(s)}} = \frac{K}{{\tau\; s} + 1}}},} & (1) \end{matrix}$ where:

Ng(s) represents a gas generator speed of the engine;

Wf(s) represents a fuel flow

τ is an estimated time constant; and

K is an estimated gain.

This relationship represented by equation (1) above may be valid for small variations around a given operating point. This operating point is typically a function of corrected gas generator speed Ng and altitude. The feedforward controller 208 designed based on equation (1) above may not require any additional tuning and testing. In some embodiments, a driving equation of the feedforward filter of the feedforward controller 208 may be given by equation (2) below:

$\begin{matrix} {{\frac{\delta\;{{Wf}_{cmd}(s)}}{\delta\;{{Ng}_{req}(s)}} = \frac{{\tau\; s} + 1}{K}},} & (2) \end{matrix}$ where:

Ng_(req) represents the requested gas generator speed; and

Wf_(cmd) represents a commanding fuel flow of the engine.

Reference is now made to FIG. 4, which shows an example feedforward controller 208 in accordance with one embodiment, implemented based on equation (3) above. The rate-limited requested gas generator speed Ngreq_(RL) 232 signal is sent to a differentiator 235. The differentiator may be for example a forward Euler derivative or any other suitable derivative function. The resulting signal S1 is multiplied at component 236 by an estimated time constant τ and divided by the estimated gain K to arrive at signal S2, which is used to generate the feedforward fuel flow WF_(FF) 217. The feedforward controller 208 is thus built based on a simplified inverse dynamic relationship of a gas generator.

The feedforward controller 208 may further take as input the rate-limited requested gas generator acceleration Ngreq_(RL)* 233 and the steady-state fuel flow WF_(SS)* 234. In some embodiments, Ngreq_(RL)* 233 is a previous value of the rate-limited gas generator speed Ngreq_(RL) 232 acquired during a previous pass. In some embodiments, WF_(SS)* 234 represents a steady state fuel flow for Ngreq_(RL)* 233. Ngreq_(RL) 232 and Ngreq_(RL)* 233 are used to generate a signal S3, which is sent to a subtraction junction 237 where the Ngreq_(RL)* 233 signal is subtracted from Ngreq_(RL) 232. The resulting signal S3 is then divided by the plant model estimated gain K at component 238 to generate signal S4. Signal S4 is summed at the summation junction 239 along with signal S2 and WF_(SS)* 234 to determine the feedforward fuel flow WF_(FF) 217, which is the output of feedforward controller 208 and is used to determine the fuel flow Nc 219 as described above.

The systems and methods described herein requires a small amount of data to be computed or obtained. For example, in some embodiments, the parameters required are the plant model estimated time constant T, plant model estimated gain K, and steady-state fuel flow WF_(SS)* 234 for a plurality of operating points of the engine. These values may be readily obtained from a data table that is stored either within or outside EEC 202. The data table may be pre-determined based on the characteristics of engine 10. For example, the values τ, K, and WF_(SS)* may be pre-populated and entered into the data table from running software simulations based on the model or other properties of engine 10. In some embodiments, the values of T, K change as a function of corrected gas generator speed Ng and/or altitude.

Accordingly, in some embodiments, EEC 202 is configured to generate a fuel flow command in accordance with a required fuel flow. EEC 202 is connected to an interface to a fuel flow metering valve for controlling the fuel flow to the engine in response to the fuel flow command. EEC 202 is configured to perform a method for controlling a gas turbine engine. An example embodiment of the method is illustrated in FIG. 5.

At step 510, EEC 202 receives a requested gas generator speed of the engine and a requested acceleration of the engine. At step 520, EEC 202 obtains a steady-state fuel flow for the requested engine speed, and the relationship between fuel flow and gas generator speed. As indicated above, the relationship may be modeled as a transfer function of equation (2) or the inverse relationship of equation (1). At step 530, EEC 202 determines the required fuel flow to obtain the requested gas generator acceleration as a function of the requested engine speed, the steady-state fuel flow, and the relationship between fuel flow and gas generator speed. At step 540, EEC 202 outputs a command to a fuel flow metering valve 204, the fuel flow metering valve 204 arranged to control a fuel flow to the engine 10.

In some embodiments, the method 500 further comprises a step of limiting acceleration of the gas turbine engine 10 by applying a rate limit to the requested engine speed, for example using rate limiter 230. In some embodiments, the required fuel flow is adjusted based on an acceleration error, for example using feedback controller 210, where the acceleration error is determined based on a reference acceleration and an actual engine acceleration determined from an actual gas generator speed.

FIG. 6 shows a schematic representation of the EEC 202, as a combination of software and hardware components in a computing device 600. The computing device 600 may comprise one or more processing units 602 and one or more computer-readable memories 604 storing machine-readable instructions 606 executable by the processing unit 602 and configured to cause the processing unit 602 to generate one or more outputs 610 based on one or more inputs 608. The inputs may comprise one or more signals representative of the requested gas generator speed, the time constant, the gain, and the steady state fuel flow. The outputs 610 may comprise one or more signals representative of the feedforward fuel flow, the feedback fuel flow, and the fuel flow command.

Processing unit 602 may comprise any suitable devices configured to cause a series of steps to be performed by computing device 600 so as to implement a computer-implemented process such that instructions 606, when executed by computing device 600 or other programmable apparatus, may cause the functions/acts specified in method 500 to be executed. Processing unit 602 may comprise, for example, any type of general-purpose microprocessor or microcontroller, a digital signal processing (DSP) processor, an integrated circuit, a field programmable gate array (FPGA), a reconfigurable processor, other suitably programmed or programmable logic circuits, or any combination thereof.

Memory 604 may comprise any suitable known or other machine-readable storage medium. Memory 704 may comprise non-transitory computer readable storage medium such as, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. Memory 604 may include a suitable combination of any type of computer memory that is located either internally or externally to computing device 600 such as, for example, random-access memory (RAM), read-only memory (ROM), compact disc read-only memory (CDROM), electro-optical memory, magneto-optical memory, erasable programmable read-only memory (EPROM), and electrically-erasable programmable read-only memory (EEPROM), Ferroelectric RAM (FRAM) or the like. Memory 604 may comprise any storage means (e.g. devices) suitable for retrievably storing machine-readable instructions 606 executable by processing unit 602.

Various aspects of the present disclosure may be embodied as systems, devices, methods and/or computer program products. Accordingly, aspects of the present disclosure may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects. Furthermore, aspects of the present disclosure may take the form of a computer program product embodied in one or more non-transitory computer readable medium(ia) (e.g., memory 604) having computer readable program code (e.g., instructions 606) embodied thereon. The computer program product may, for example, be executed by a computer to cause the execution of one or more methods disclosed herein in entirety or in part.

Computer program code for carrying out operations for aspects of the present disclosure in accordance with instructions 606 may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or other programming languages. Such program code may be executed entirely or in part by a computer or other data processing device(s). It is understood that, based on the present disclosure, one skilled in the relevant arts could readily write computer program code for implementing the methods disclosed herein.

The above description is meant to be exemplary only, and one skilled in the relevant arts will recognize that changes may be made to the embodiments described without departing from the scope of the invention disclosed. For example, the blocks and/or operations in the flowcharts and drawings described herein are for purposes of example only. There may be many variations to these blocks and/or operations without departing from the teachings of the present disclosure. For instance, the blocks may be performed in a differing order, or blocks may be added, deleted, or modified. The structure illustrated is thus provided for efficiency of teaching the present embodiment. The present disclosure may be embodied in other specific forms without departing from the subject matter of the claims. Also, one skilled in the relevant arts will appreciate that while the systems, methods and computer readable mediums disclosed and shown herein may comprise a specific number of elements/components, the systems, methods and computer readable mediums may be modified to include additional or fewer of such elements/components. The present disclosure is also intended to cover and embrace all suitable changes in technology. Modifications which fall within the scope of the present invention will be apparent to those skilled in the art, in light of a review of this disclosure, and such modifications are intended to fall within the appended claims. 

The invention claimed is:
 1. A system for controlling a gas turbine engine of an aircraft, the system comprising: an interface to a fuel flow metering valve for controlling a fuel flow to the engine in response to a fuel flow command; and a controller connected to the interface and configured for outputting the fuel flow command to the fuel flow metering valve in accordance with a required fuel flow, the controller comprising a feedforward controller configured for: receiving a requested engine speed and a requested engine acceleration; obtaining a steady-state fuel flow for the requested engine speed and a relationship between fuel flow and gas generator speed; and determining the required fuel flow to obtain the requested engine acceleration as a function of the requested engine speed, the steady-state fuel flow, and the relationship between fuel flow and gas generator speed.
 2. The system of claim 1, wherein the controller is further configured to limit acceleration of the gas turbine engine by applying a rate limit to the requested engine speed.
 3. The system of claim 1, wherein the controller comprises a feedback controller configured to adjust the required fuel flow based on an acceleration error.
 4. The system of claim 3, wherein the acceleration error is determined based on a requested engine acceleration and an actual engine acceleration determined from an actual gas generator speed.
 5. The system of claim 1, wherein the feedforward controller is configured to obtain the steady state fuel flow for the requested engine speed from a look-up table.
 6. The system of claim 1, wherein determining the required fuel flow comprises applying the equation: ${\frac{\delta\;{{Ng}(s)}}{\delta\;{{Wf}(s)}} = \frac{K}{{\tau\; s} + 1}},$ where: Ng(s) represents a gas generator speed of the engine at a given operating point s; Wf(s) represents a fuel flow of the engine at the given operating point; τ is a time constant of a transfer function between the fuel flow and the gas generator speed; and K is a gain of the transfer function between the fuel flow and the gas generator speed.
 7. The system of claim 6, wherein the given operating point is a function of a corrected gas generator speed and altitude of the aircraft.
 8. The system of claim 1, wherein determining the required fuel flow comprises applying the equation: ${\frac{\delta\;{{Wf}_{cmd}(s)}}{\delta\;{{Ng}_{req}(s)}} = \frac{{\tau\; s} + 1}{K}},$ where: Ng_(req)(s) represents the requested gas generator speed at a given operating point s; Wf_(cmd) represents an output of the feedforward controller at the given operating point s for the requested gas generator speed; τ is a time constant of a transfer function between the fuel flow and the gas generator speed; and K is a gain of the transfer function between the fuel flow and the gas generator speed.
 9. A method for controlling a gas turbine engine, the method comprising: receiving a requested engine speed and a requested engine acceleration; obtaining a steady-state fuel flow for the requested engine speed and a relationship between fuel flow and gas generator speed; determining the required fuel flow to obtain the requested engine acceleration as a function of the requested engine speed, the steady-state fuel flow, and the relationship between fuel flow and gas generator speed; and outputting a command to a fuel flow metering valve in accordance with the required fuel flow.
 10. The method of claim 9, further comprising limiting acceleration of the gas turbine engine by applying a rate limit to the requested engine speed.
 11. The method of claim 9, further comprising adjusting the required fuel flow based on an acceleration error.
 12. The method of claim 11, wherein the acceleration error is determined based on a requested engine acceleration and an actual engine acceleration determined from an actual gas generator speed.
 13. The method of claim 9, wherein the steady state fuel flow for the requested engine speed is obtained from a look-up table.
 14. The method of claim 9, wherein determining the required fuel flow comprises applying the equation: ${\frac{\delta\;{{Ng}(s)}}{\delta\;{{Wf}(s)}} = \frac{K}{{\tau\; s} + 1}},$ where: Ng(s) represents a gas generator speed of the engine at a given operating point s; Wf(s) represents a fuel flow of the engine at the given operating point; τ is a time constant of a transfer function between the fuel flow and the gas generator speed; and K is a gain of the transfer function between the fuel flow and the gas generator speed.
 15. The method of claim 14, wherein the given operating point is a function of a corrected gas generator speed and altitude of the aircraft.
 16. The method of claim 9, wherein determining the required fuel flow comprises applying the equation: ${\frac{\delta\;{{Wf}_{cmd}(s)}}{\delta\;{{Ng}_{req}(s)}} = \frac{{\tau\; s} + 1}{K}},$ where: Ng_(req)(s) represents the requested gas generator speed at a given operating point s; Wf_(cmd) represents an output of the feedforward controller at the given operating point s for the requested gas generator speed; τ is a time constant of a transfer function between the fuel flow and the gas generator speed; and K is a gain of the transfer function between the fuel flow and the gas generator speed.
 17. A non-transitory computer-readable medium having stored thereon program code executable by a processor for controlling a gas turbine engine, the program code comprising instructions for: receiving a requested engine speed and a requested engine acceleration; obtaining a steady-state fuel flow for the requested engine speed and a relationship between fuel flow and gas generator speed; determining the required fuel flow to obtain the requested engine acceleration as a function of the requested engine speed, the steady-state fuel flow, and the relationship between fuel flow and gas generator speed; and outputting a command to a fuel flow metering valve in accordance with the required fuel flow.
 18. The non-transitory computer-readable medium of claim 17, wherein the program code further comprises instructions for limiting acceleration of the gas turbine engine by applying a rate limit to the requested engine speed.
 19. The non-transitory computer-readable medium of claim 17, wherein the program code further comprises instructions for adjusting the required fuel flow based on an acceleration error.
 20. The non-transitory computer-readable medium of claim 17, wherein determining the required fuel flow comprises applying the equation: ${\frac{\delta\;{{Wf}_{cmd}(s)}}{\delta\;{{Ng}_{req}(s)}} = \frac{{\tau\; s} + 1}{K}},$ where: Ng_(req)(s) represents the requested gas generator speed at a given operating point s; Wf_(cmd) represents an output of the feedforward controller at the given operating point s for the requested gas generator speed; τ is a time constant of a transfer function between the fuel flow and the gas generator speed; and K is a gain of the transfer function between the fuel flow and the gas generator speed. 